shuttle under various conditions as it landed. The computer was the only way to solve
such problems without real-life testing. It quickly and easily solved a plethora of
mathematical equations—especially calculus and differential equations—that repre-
sented how the shuttle would take off, fly, and land.What is fluid mechanics?
Fluids are substances that flow, including gases and liquids. Fluid mechanics, or
hydraulics, is the study of the physical behavior of these gases and liquids and their
role in engineering systems. This includes the mathematics of the forces in and
motion of substances, turbulence, wave propagation, and so on.
Most fluid mechanics problems in engineering are mathematically modeled using
differential equations. These models can also be applied to other engineering areas,
such as electromagnetism and the mechanics of solids (because solids still “move,”
albeit slowly). Other fluid mechanical studies include the compressibility of sub-
stances. In most cases, liquids are considered to be incompressible and gases are con-
sidered to be compressible. But there are exceptions in some everyday engineering
applications, and they can easily be explored using mathematical modeling.
Engineers also use special mathematical equations to determine certain charac-
328 teristics of fluid flow, such as whether the flow is slow and smooth (laminar) or turbu-
Who was Oliver Heaviside?
E
nglish electrical engineer Oliver Heaviside (1850–1925) was a self-taught
genius who made several contributions to the field of electricity and even
atmospheric studies. In 1902 Heaviside predicted that there was a conducting
layer in the atmosphere that allowed radio waves to follow the Earth’s curva-
ture—a layer now named after him.In electrical engineering, Heaviside was best known for operational calcu-
lus,a tool for solving linear differential equations with constant coefficients. It
was usually applied to brief or fleeting (called transient) phenomena and was
very similar to Laplace transform in its calculations. Although Laplace had
developed his ideas almost a century before, Heaviside knew nothing of them,
because they were not well-known during his time.But Heaviside’s operational calculus did have its problems, as well as its crit-
ics. It was severely limited because of its lack of mathematical theory. This not
only limited its applications, but also created many uncertainties and ambigui-
ties in the equations and solutions. Today, operational calculus has been
replaced by Laplace transform, especially in fields such as electrical engineering.